Solve for $x$ : $4x^2 + 48x + 80 = 0$
Dividing both sides by $4$ gives: $ x^2 + {12}x + {20} = 0 $ The coefficient on the $x$ term is $12$ and the constant term is $20$ , so we need to find two numbers that add up to $12$ and multiply to $20$ The two numbers $2$ and $10$ satisfy both conditions: $ {2} + {10} = {12} $ $ {2} \times {10} = {20} $ $(x + {2}) (x + {10}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 2) (x + 10) = 0$ $x + 2 = 0$ or $x + 10 = 0$ Thus, $x = -2$ and $x = -10$ are the solutions.